The conductivity enhancement in superionic conductors with dispersed dielectrics has been interpreted to be due to the formation of thin boundary regions between the superionic conducting and the dispersed dielectric materials. To examine the role playd by surfaces or boundaries, we have tried to make AgI thin films on glass plates and see the thickeness dependence of conductivity.We could indeed make AgI thin films by flowing iodine gas on Ag films, vacuum-deposited on a glass plate. Electron microscope was used to examine films of thickness about 100A, and the formation of AgI was confirmed. The conductivity has been measured in films of various thickness in the frequency range 1kHz-10MHz. Unfortunately, no notable and reproducible thickness dependence of conductivity was observed.In all, so far we have not been able to make clear the role playd by surfaces and boundaries in the conductivity enhancement. But we would like to pursuit the phenomenon further, since the enhancement of conductivity seems to be important from the application vewpoint.